<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01//EN" "http://www.w3.org/TR/html4/strict.dtd">
<html>
<head>
<title></title>
<!--Generated on Mon Oct 27 10:47:59 2014 by LaTeXML (version 0.7.999_04) http://dlmf.nist.gov/LaTeXML/.-->

<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<link rel="stylesheet" href="../../../../../../LaTeXML.css" type="text/css">
<link rel="stylesheet" href="../../../../../../ltx-article.css" type="text/css">
<link rel="stylesheet" href="../../../../../../customRules.css" type="text/css">
</head>
<body>
<div class="ltx_page_main">
<div class="ltx_page_content">
<div class="ltx_document">
<div id="Sx1" class="ltx_section">
<h1 class="ltx_title ltx_title_section">Polynomial defocusing model</h1>

<div id="Sx1.p1" class="ltx_para">
<p class="ltx_p">The default model used in ThunderSTORM describes the relationship
between the axial position of a molecule and its imaged widths along
two perpendicular axes by a pair of second degree polynomials</p>
<table id="Sx1.EGx1" class="ltx_equationgroup ltx_eqn_eqnarray">

<tr id="Sx1.Ex1" class="ltx_equation ltx_align_baseline">
<td class="ltx_eqn_pad"></td>
<td class="ltx_td ltx_align_right"><img id="Sx1.Ex1.m1" class="ltx_Math" style="vertical-align:-6px" src="mi/mi3.png" width="48" height="21" alt="\displaystyle\sigma_{1}\left(z\right)"></td>
<td class="ltx_td ltx_align_center"><img id="Sx1.Ex1.m2" class="ltx_Math" style="vertical-align:-2px" src="mi/mi1.png" width="18" height="11" alt="\displaystyle="></td>
<td class="ltx_td ltx_align_left"><img id="Sx1.Ex1.m3" class="ltx_Math" style="vertical-align:-6px" src="mi/mi6.png" width="136" height="25" alt="\displaystyle a_{1}\left(z-c_{1}\right)^{2}+b_{1}\,,"></td>
<td class="ltx_eqn_pad"></td>
</tr>
<tr id="Sx1.Ex2" class="ltx_equation ltx_align_baseline">
<td class="ltx_eqn_pad"></td>
<td class="ltx_td ltx_align_right"><img id="Sx1.Ex2.m1" class="ltx_Math" style="vertical-align:-6px" src="mi/mi5.png" width="48" height="21" alt="\displaystyle\sigma_{2}\left(z\right)"></td>
<td class="ltx_td ltx_align_center"><img id="Sx1.Ex2.m2" class="ltx_Math" style="vertical-align:-2px" src="mi/mi1.png" width="18" height="11" alt="\displaystyle="></td>
<td class="ltx_td ltx_align_left"><img id="Sx1.Ex2.m3" class="ltx_Math" style="vertical-align:-6px" src="mi/mi7.png" width="136" height="25" alt="\displaystyle a_{2}\left(z-c_{2}\right)^{2}+b_{2}\,."></td>
<td class="ltx_eqn_pad"></td>
</tr>
</table>
<p class="ltx_p">Here <img id="Sx1.p1.m1" class="ltx_Math" style="vertical-align:-5px" src="mi/mi8.png" width="68" height="19" alt="a_{1},b_{1},c_{1}"> and <img id="Sx1.p1.m2" class="ltx_Math" style="vertical-align:-5px" src="mi/mi9.png" width="68" height="19" alt="a_{2},b_{2},c_{2}"> are unknown parameters
of the model which can be determined by the calibration process.</p>
</div>
<div id="Sx1.SSx1" class="ltx_subsection">
<h2 class="ltx_title ltx_title_subsection">See also</h2>

<div id="Sx1.SSx1.p1" class="ltx_para">
<ul id="I1" class="ltx_itemize">
<li id="I1.i1" class="ltx_item" style="list-style-type:none;">
<span class="ltx_tag ltx_tag_itemize">•</span> 
<div id="I1.i1.p1" class="ltx_para">
<p class="ltx_p"><a href="DefocusModels.html" title="" class="ltx_ref">Defocusing models</a></p>
</div>
</li>
<li id="I1.i2" class="ltx_item" style="list-style-type:none;">
<span class="ltx_tag ltx_tag_itemize">•</span> 
<div id="I1.i2.p1" class="ltx_para">
<p class="ltx_p"><a href="../estimators/ui/EllipticGaussianEstimatorUI.html" title="" class="ltx_ref">Rotated elliptical Gaussian function PSF model (3D using astigmatism)</a></p>
</div>
</li>
<li id="I1.i3" class="ltx_item" style="list-style-type:none;">
<span class="ltx_tag ltx_tag_itemize">•</span> 
<div id="I1.i3.p1" class="ltx_para">
<p class="ltx_p"><a href="../estimators/ui/CalibrationEstimatorUI.html" title="" class="ltx_ref">Calibration of the imaging system</a></p>
</div>
</li>
</ul>
</div>
</div>
</div>
</div>
</div>
<div class="ltx_page_footer">
<div class="ltx_page_logo">Generated  on Mon Oct 27 10:47:59 2014 by <a href="http://dlmf.nist.gov/LaTeXML/">LaTeXML <img src="" alt="[LOGO]"></a>
</div>
</div>
</div>
</body>
</html>
